While playing, if you hit X, your menu will pop up. Scroll over to the Save Icon (it will say "Save" as you scroll over it) and hit C. It will then prompt you about saving the game, to which you select yes. After you have saved, you may close the game and when you re-open it later, your save file will be loaded up for you.

Note: The buttons I listed are assuming you did not remap the controls. If you did remap them, X corresponds to whatever opens your menu, and C is whatever you use to select things/do actions.